Question

If f:R→R is given by f(x)=(5+x^4)^1/4, then fοf(x) is _______

(a) x

(b) 10+x^4

(c) 5+x^4

(d) (10+x^4)^1/4

This question was posed to me during an online exam.

I'm obligated to ask this question of Composition of Functions and Invertible Function topic in section Relations and Functions of Mathematics – Class 12

Answer 1

Correct option is (d) (10+x^4)^1/4

The explanation: Given that f(x)=(5+x^4)^1/4

∴ fοf(x)=f(f(x))=(5+{(5+x^4)^1/4}^4)^1/4

=(5+(5+x^4))^1/4=(10+x^4)^1/4.